Construction of Selection Indices and their Uses | Animal Husbandry & Veterinary Science Optional for UPSC PDF Download

Introduction

A selection index represents the optimal linear prediction of an individual's breeding value, formulated as a multiple regression of breeding values on available information. In its simplest form, with only the individual's phenotypic value (P) as information, the predicted breeding value is denoted as (A)-bar P, where (A)-bar is the regression of breeding value on phenotypic value.

Utilization of Multiple Phenotypic Measurements

• Considering situations with multiple pieces of information (P, P₁, P₂, etc.), each representing the phenotypic value of an individual or a group of relatives, the selection index for an individual is expressed as:
  I = b₀P + b₁P₁ + b₂P₂ + ...
• Here, b₀, b₁, b₂, etc., are the weighting factors for each measurement. The objective is to determine the optimal values for these weighting factors by maximizing the correlation between the index and the breeding value. This process involves minimizing the sum of squared deviations of index values from the linear regression of the index on breeding value (Z-A). The resulting values of b₀, b₁, b_2, etc., are the partial regression coefficients for each measurement, indicating their impact on the individual's breeding value.

Calculation of Weighting Factors

The calculation involves solving a set of simultaneous equations, where the number of equations corresponds to the number of measurements. The solution provides the values of the weighting factors (b₀, b₁, b₂,) for the equation. The standard procedure for calculating partial regressions, and maximizing the correlation, leads to these simultaneous equations.

Equations for Solution:

• The equations, given for three measurements as an example, are extended or reduced based on the number of measurements. Each equation relates phenotypic variances and covariances of the measurements to the additive genetic variances and covariances of the individuals measured. 
• The condensed notation is used, where P denotes the phenotypic variance or covariance of the measurements.
• The equations for solution are expressed in terms of phenotypic variances and covariances (P) and additive genetic variances and covariances (A).

• To solve these equations, numerical values for the phenotypic (P) and additive genetic (A) parameters must be inserted. Expressing all Ps and As in terms of specific parameters, including the phenotypic variance (denoted as σ), heritability of individual value, phenotypic correlation between individuals, and coefficient of relationship, is crucial. Additionally, when measurements represent the means of groups, the number (n) in each group is required. Standard computer programs are available for efficiently solving these equations.
• The application of indices can be demonstrated through specific examples, simplifying the discussion by considering only two measurements – individuals and one relative. For instance, a mother and one paternal half-sister or an individual and the mean of a sibling group.

In the context of improving the economic value of animals or plants through selection, the focus is often on multiple traits simultaneously. This approach, known as multiple trait selection, recognizes that economic value depends on more than one character. For example, the profitability of a pig herd is influenced by factors such as fertility, mothering ability, growth rate, food utilization efficiency, and carcass qualities. Various methods exist for applying selection to maximize the improvement of economic value. However, the most effective approach is often simultaneous selection for all components, assigning appropriate weights based on their relative economic importance, heritability, and genetic and phenotypic correlations. These component characters are then combined into a score or index, enabling selection for the index to yield the most rapid improvement in economic value. The breeding value is predicted for a composite of several characters evaluated in economic terms. This composite, representing the objective of selection referred to as "merit," is symbolized by H, and the index constructed for the improvement of merit is the key focus.

Here, P1 to Pm represents the phenotypic measurements of m characters, forming the basis for selection, and the corresponding weights (b1 to bm) are yet to be determined. The b's denote the partial regression coefficients of the overall merit (H) on the selection index (I). It's noteworthy that information from relatives can be incorporated into the index, allowing the measurements (P's) to include data from relatives.

Single Traits:

Let's first consider a selection focused on enhancing a single character. In this context, employing an index for selection means using secondary characters as aids to improve the primary desired trait. The equations for the index, whose solution determines the values of the b's, are exactly the same as those provided in the following page, with character 1 as the trait targeted for improvement.

Here P₁₁ is the phonotypic vengeance of character 1, and P₁₂ is the phase type covariance of characters 1 and 2. A₁₁ and A₂₁ are similar to the additive genetic variance and covariance The variances and covariances can be agreed in terms of the heritabilities and correlation as follows, where the script I and j refer to any two different characters and o² is the phenotype variance.

When the values of this and covariance have been entered, the elution of equations (4) provides the values of the weighting factors, b, to be used in the index in the equation.

Economic Value:

The economic value of an individual is essentially the profit derived from its sale. In practical breeding operations, it is often feasible to assign economic values to individuals. In such cases, the economic value becomes the phenotypic value of merit, representing the trait targeted for improvement. Consequently, the index is formulated specifically for the enhancement of this singular trait. However, the equations for the index, providing the values for the coefficients (b's), differ from the previously described scenario. Notably, the economic values of individuals cannot be determined at the time of selection consideration and, therefore, cannot be directly included as a character in the index. For ease of comparison, let's consider character 1 as the trait to be improved, or in this case, the merit itself.

Estimations of variances, both for the economic values and the character values included in the index, need to be derived from historical records.

Multiple traits:

Finally, consider simultaneous selection for several characters. The objective is to improve the breeding value or not merits, which is a particular combustion of all the characters to be improved. Merit is defined as

Here, the A values represent breeding values for the n characters targeted for improvement, while the a's are weighting factors signifying the relative importance assigned by the breeder to each character. These weighting factors can also be expressed as economic values.

• The number of characters defining merit (H) and those included in the index may not be identical. Some characters might not be part of H but can contribute to its improvement through correlations if included in the index (I). Conversely, there could be characters in H that are unmeasurable and therefore not included in I. If the goal is to enhance economic value, all characters influencing economic value must be incorporated into the definition of H.
• The equations for the index, determining the values of the weights (b's) used in the index, are derived in the same manner as obtaining equations 1 and 2. This process involves maximizing the correlation between merit and the index, and they are subsequently expressed.

• The variances and covariances can gain be expressed in terms of the heritability and correlations of equation (5).